In a walk fir charity,you. Walk at a rate of 100 meters per minute.how long does it take you to walk 2 kilometers

The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral

Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have $y_4 - y_3$ so one side is CD. The other side must be BC or AD; AD would give $y_4 - y_1$ terms which don't appear among the answer, so let's go with BC.

The direction vectors are

$D-C = (x_4 - x_3, y_4 - y_3)$

$C-B = (x_3 - x_2, y_3 - y_2)$

For perpendicularity we need a zero dot product:

$0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)$

$- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)$

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

8 0

3 years ago

Gwen takes out a loan of $400 to pay for an online course. Flat rate interest is charged at 8% p.a

puteri [66]

We know, 1 year = 12 month.

So, 3 month = 3/12 = 0.25 year.

Now, principle amount, P = $400 .

Rate is, r = 8% = 0.08

Time period, t = 0.25 year.

Now, Interest is given by :

I = P × r × t

I = $( 400 × 0.08 × 0.25 )

I = $8

Therefore, she will pay $8 interest in total.

5 0

3 years ago

4.

sveticcg [70]

(a)The domain of the function is, $\rm x \geq -c^2 \ x\neq0$

(b)The given function is discontinuous at x=0.

<h3>What is the domain and range of a function?</h3>

Domain is the set of values for which the given function is defined. Range is the set of all values which the given function can output.

The standard function is;

$\rm f(x)= \frac{\sqrt{x+c^2-c} }{x} , c > 0$

The domain of the given function is found as;

$\rm x+c^2 \geq 0 \ x\neq 0 \\\\ x\geq-c^2 \ x\neq 0$

The domain of the function is,

$\rm x \geq -c^2 \ x\neq0$

To find the function is continuous or not, we have to find the continuity;

$\rm f(x) = \frac{\sqrt{ x+c^2-c}}{x} ,c > 0$

At x= 0 the function is undefined. So that the function is discontinuous at x=0.

Hence, The domain of the function is, $\rm x \geq -c^2 \ x\neq0$ and the function is discontinuous at x=0.

To learn more about domain, refer to the link:

brainly.com/question/20073127

#SPJ1

7 0

3 years ago

Which is the simplified form of n Superscript negative 6 p cubed?

evablogger [386]

Answer:

Third option. $\frac{p^3}{n^{6}}$

Step-by-step explanation:

For this exercise you need to remember one of the properties for exponents.

There is a property called the "Negative property of exponents" which states the following:

$b^{-n}=\frac{1}{b^n}$

Where $b \neq0$

As you can observe, $b^n$ is the reciprocal of $b^{-n}$

In this case you have the following expression given in the exercise:

$n^{-6}p^3$

Observe the expression. As you can notice, the base "n" has a negative exponent, which is -6.

Therefore, applying the Negative property of exponents explained at the beginning of this explanation, you can simplify the expression.

Then, the simplified form of $n^{-6p^3}$ is the one shown below:

$n^{-6}p^3=\frac{p^3}{n^{6}}$

3 0

3 years ago

Read 2 more answers

Carrie ate some of the oranges that her mother brought home from the grocery store of the oranges her mother bought 1/4 were lef

Whitepunk [10]

From the given scenario, it can be deduced that Carrie ate 3/5 of what was left of the oranges that were left. To determine the fraction that Carrie ate, we will multiply 3/5 by 1/4. This is equal to 3/20. Thus, Carrie ate approximately 3/20 of the oranges left.

3 0

3 years ago